by one or two satellite peaks on the higher–
binding energy side (Figs. 1 and 4, with details
provided in the supplementary materials). At
the lowest alkali metal concentrations, the
solvated electron peak can be fitted to a Gaussian
function (Fig. 4) with a full width at half
maximum of about 0.45 to 0.6 eV [i.e., slightly
narrower than the equivalent first ionization
peak for halides in liquid ammonia ( 49 )] and
with a low energy onset (appearance potential)
at ~1.5 eV, which is close to the previous esti-
mate of 1.4 eV from the PE threshold measure-
ments ( 24 , 25 ).
By contrast, at the highest lithium concentra-
tion of 9.7 MPM, the PE spectrum is fitted to an
inverse-parabola conduction band with a sharp
Fermi edge and two plasmon peaks (Fig. 4),
as follows directly from the free-electron gas
model for metals ( 58 ), with an effective electron
mass close to unity (Fig. 4 and Table 1). Owing to
the relatively low electron density, the plasmon
frequency is in the visible range, which gives
the concentrated alkali metal–ammonia so-
lutions their characteristic bronze or gold color
( 1 , 59 ). A conduction band with a Fermi edge
and a plasmon peak can also be observed for
the 1.25 MPM potassium–ammonia solution,
whereas for sodium–ammonia we could notprepare homogeneous solutions above ~1 MPM
because of spontaneous phase separation at
the experimental conditions ( 1 , 2 ).
An analogous fit to a free-electron gas model
is shown for a microjet PE spectrum of liquidButtersacket al.,Science 368 , 1086–1091 (2020) 5 June 2020 4of6
Fig. 4. Analysis and fits of the PE spectra in the
electrolyte and metallic regimes.Partial fits
to the conduction band, plasmons, and localized
(di)electrons are vertically offset for visual clarity.
(A) Fit (relative root mean square error of 5.3%) of
the liquid Na–K alloy to a free-electron gas model.
At low binding energy, we observe a Fermi edge
leading feature with the characteristic parabolic
shape of the conduction band; plasmon excitations
are seen at higher binding energies. (B) Fits (relative
root mean square errors of 6.3, 6.8, 7.1, 8.9, and
32.2% for 9.7, 3.4, 0.97, 0.35, and 0.08 MPM,
respectively) of Li–NH 3 data to a combination, in
varying ratios, of a free-electron gas model with
plasmon bands for the fraction where the electron
is delocalized and a single Gaussian function to
represent the localized (di)electron. (C) Evolution of
the liquid ammonia 3a 1 peak upon increasing Li
concentration. (D) Concentration dependence of the
effective electron mass from fits in (A) and (B).
(E) Relative peak areas corresponding to the
localized Gaussian, the conduction band, and the
plasmon peaks in (B). wrt, with respect to;EF, Fermi
energy; vac, vacuum;m*, effective electron mass;
me, stationary electron mass.Table 1. Key parameters for lithium–ammonia solutions and the sodium–potassium alloy.
c, concentration;ne, electron density;me*, effective electron mass;me, stationary electron mass.
Widths of the conduction band (Ec) and positions of the plasmon peak (EP) are expressed with
respect to the Fermi energy (EF).EcandEPwere determined from fitting to a free-electron gas model
with the effective electron masses given in the table. The effective electron massesme* were
obtained by fitting as described in the supplementary materials.–, not determined.Parameter NaK Li@NH 3 Li@NH 3 Li@NH 3 Li@NH 3 Li@NH 3 Li@NH 3
c.....................................................................................................................................................................................................................(MPM) 100 9.7 3.4 0.97 0.35 0.08 0.012
c.....................................................................................................................................................................................................................(M) 29 4.3 1.4 0.39 0.14 0.03 0.005
n.....................................................................................................................................................................................................................e(×10^21 cm−^3 ) 16.3 2.15 1.05 0.25 0.09 0.02 0.003
m.....................................................................................................................................................................................................................e*/me 1.21 0.72 0.49 0.25 –––
E.....................................................................................................................................................................................................................c(eV) 2.06 0.85 0.74 0.98 –––
E.....................................................................................................................................................................................................................P(eV) 4.52 2.03 1.67 1.74 –––RESEARCH | RESEARCH ARTICLE